Tetragonal high-pressure phase of ZnO predicted from first principles

We report a high-pressure tetragonal PbO-type structure $\left(B10\right)$ of ZnO predicted through ab initio lattice-dynamics calculation. This structure can be directly transformed from NaCl structure $\left(B1\right)$ along an orthorhombic $Pmmn$ transition path and can be viewed as alternatively stacked layers of cations and anions with the anion layer composed of zigzag arranged anionic rows. Enthalpy curve calculation suggests that $B10$ is stable in a large pressure range of 236–316 GPa, above which CsCl structure $\left(B2\right)$ takes over. Band-structure calculation reveals that this polymorph is a wide band-gap semiconductor with an energy gap larger than 2.95 eV.

Figure 1

(Color online) (a) The calculated $P\text{−}V$ relation for $B1$ phase together with experimental data from Desgreniers (Ref. 7) and Liu et al. (Ref. 12). The theoretical $P\text{−}V$ curve is derived by fitting the calculated volume vs energy data into the Murnaghan equation of sate. (b) Enthalpy of $B1$ and $B10$ relative to that of $B2$. The $B10$ phase is more stable than $B1$ above 236 GPa and converges with $B2$ above 316 GPa. (c) Phonon dispersion curves of $B2$ at 250 GPa. (d) Evolution of the $\text{TA}\left(M\right)$ phonon frequency with increasing pressures. The vertical solid line marks the critical pressure above which $B2$ becomes dynamically stable.

Figure 2

(Color online) (a) The dashed unit cell is a $2\times 2\times 1$ supercell of $B2$ structure. Oxygen (small sphere) atomic distortion along the eigenvector of $\text{TA}\left(M\right)$ mode as indicated by the arrows results in the formation of $B10$ phase (solid unit cell). (b) Top view of the $B10$ structure along the [010] direction. (c) Energy evolution curves with the oxygen displacements along the eigenvector of $\text{TA}\left(M\right)$ mode at 200, 250, 320, and 360 GPa, respectively. The total energies are normalized to that of $B2$ for comparison.

Figure 3

(Color online) (a) Energy band structure of $B10$ at 250 GPa. (b) Phonon dispersion curves of $B1$ along the $\Gamma \text{−}X\text{−}K$ direction at 250 GPa. (c) Energy evolution curves with respect to the shearing displacements of (001) planes in $B1$ at 290 GPa along three different directions of [010], [310], and [110]. The distorted structures along the three directions have the space groups of $Cmcm$, $P{2}_1/m$, and $Pmmn$, respectively. Displacements have been scaled to the lattice parameter $a_0$ of $B1$. Note that energy curves with other displacement directions lie in between [010] and [110] with all of the distorted structures having space group of $P{2}_1/m$.

Figure 4

(Color online) Schematic representation of the $B1\to B10$ transformation in a $1\times 1\times 2$ supercell of $Pmmn$ structure. Lattice parameters $a$, $b$, and $c$ of the $Pmmn$ structure are labeled, and the [100], [010], and [110] crystal directions of the pristine $B1$ structure are also shown for comparison. The $B10$ and $Pmmn$ structures share the same crystal orientation. The antiparallel shuffle movement (indicated by arrows) of adjacent (001) planes of $B1$ along the ${\left[110\right]}_{B1}$ direction causes the zinc (large gray sphere) and oxygen (small black sphere) ions to detach from each other along the $c$ axis and results in the formation of $B10$ structure with separated cation and anion layers.